By virtue of the generalized L'Hôpital's rule [1]}, \(p_{m,k}^{out}\)  can be obtained as
\(&p_{m,k}^{out}= \frac{1}{{\Gamma \left( {{N_r} - M + 1} \right)}}{\frac{{{\partial ^{{N_r} - 1}}}}{{\partial {\lambda }^{{N_r} - 1}}}\Biggl [ {{\lambda }^{{N_r} - 1}}\times }\\&\,\,\,\,\,{ {G_{2,3}^{2,1}\left( {\left. {\begin{array}{*{20}{c}}{1,{N_r}}\\{1,{N_r} - M + 1,0}\end{array}} \right|\frac{{{{\left[ {{{\bf {R}}_{t^{\prime }}}^{ - 1}} \right]}_{mm}}}}{{{\lambda }\bar{\gamma }{\theta _{m,k}}\ell ({d_k})}}} \right)} \Biggr ]_{{\lambda } = {\lambda _0}}}.\) 
